Orientador: Amauri Hassui / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-21T02:13:50Z (GMT). No. of bitstreams: 1 Castro_MarceloHirai_M.pdf: 4008200 bytes, checksum: a0c71450e4b5c3ac934e22f6e3cc9f4b (MD5) Previous issue date: 2012 / Resumo: A inovação é a chave para o diferencial da indústria no mercado competitivo atual. Fazer diferente, melhor e mais barato sempre agrega valor ao produto. Por outro lado, a resistência às mudanças faz parte do comportamento humano, seja na sociedade, ou na indústria. O objetivo principal deste trabalho é estudar a viabilidade de se fazer furos não cilíndricos com uma ferramenta em rotação utilizando máquinas-ferramenta CNC. Estes sempre foram obstáculos na indústria de fabricação pela dificuldade de obtenção. Sendo assim, o processo apresentado nesse trabalho busca usinar um furo quadrado com a mesma configuração de ferramentas e fixação de peças utilizadas para um furo cilíndrico, tão comum à indústria. Isso visa reduzir custos de fabricação e facilitar a obtenção de furos não cilíndricos com os recursos de equipamentos programáveis existentes no chão de fábrica. A partir de um modelo matemático, a máquina é programada para executar movimentos sincronizados entre a rotação e os deslocamentos do eixo da ferramenta. Diversas programações foram testadas em diferentes máquinas ferramenta CNC, com diferentes comandos, com e sem recursos de alta velocidade, com diferentes quantidades de pontos programados, interpolações lineares e circulares. A partir dos experimentos, foram analisadas as configurações das máquinas, a capacidade de execução do controlador numérico instalado, a velocidade desenvolvida pela máquina na operação e a geometria obtida dos furos quadrados. Os experimentos apontam que para executar o furo quadrado, os comandos devem ser capazes de controlar um eixo rotativo como eixo propriamente dito, além de sincronizarem mais três eixos lineares. O crítico para este tipo de operação é a velocidade desempenhada pela máquina, sendo o fator mais significativo, o tempo que o comando precisa para o processamento do bloco de programação, independentemente da ativação de recursos de alta velocidade, interpolações lineares ou circulares. Verificou-se também que quanto maior a quantidade de pontos para compor a trajetória do centro da ferramenta, melhor será a geometria obtida do furo. Sendo assim, as máquinas ferramenta CNC que estão em operação na indústria são capazes de realizar a furação não cilíndrica de forma muito próxima à furação cilíndrica quanto ao tempo de usinagem e ao sistema de fixação da ferramenta e da peça, sendo necessária uma programação sincronizada do eixo spindle presente em toda e qualquer máquina ferramenta / Abstract: The innovation is the key for the differential of the industry on the competitive market nowadays. To make different, better and cheaper always it is worth a lot to the product. By the other side, the resistance to changes makes part of the human behavior, in society, or in the industry. The main goal of this work is to study the feasibility to machining of non-cylindrical holes by a tool in rotation using CNC machine tools. That always has been offering obstacles to manufacturing industry by the difficulty of fabrication. Thus, the process presented on this work will machining a square hole with the same configuration of tools and systems for fixation of the parts, used for a cylindrical drilling, so common to industry. This intends to reduce the costs of fabrication and make easier to get non-cylindrical drilling using resources of the programmable equipment which are working at the shops. From a math model on, the machine is programmed to execute synchronized movements between the rotation and the displacements of the axis of the tool. Different programs were tested in different CNC machine tools, with different controllers, with and no resources for high speed, with different quantity of programmed points, with linear and circular interpolations. From the experiments, it was analyzed the configuration of the machines, the capacity for execution of the controller installed, the speed developed by machine at the operation and the geometry of the square holes. The experiments show that to machine a square hole, the controllers must be able to control a rotating axis itself, beyond to synchronize three axis. The critical to this kind of operation is the speed developed by the machine, being the most significant factor, the time the controller needs to process the block of programming, independently the activation of resources for high speed, linear or circular interpolations. It was verified than as larger the amount of points to compose the trajectory of the center of tool, better will be the geometry of the hole. Thus, the CNC machine tools in operation in the industry are able to machine the non-cylindrical drilling in a way very closely the cylindrical drilling as the time of machining and the fixing system of the tool and parts, requiring a programming that synchronizes the main spindle installed in any machine tool / Mestrado / Materiais e Processos de Fabricação / Mestre em Engenharia Mecânica

Vevaxeldeformation studeras i samband med uppspänning i en virvelfräsmaskin inför en skärande process. Syftet är att öka förståelse om deformationsbeteendet av vevaxelns viktiga funktionsytor genom analysering med Finita elementmetoden (FEM). Volvo Cars i Skövde hanterar i dagsläget oönskad vevaxeldeformation genom tidskrävande fysiska tester. Därför önskar företaget ta stöd av virtuell analysering. Detta arbete leder även till ett fastställande om FEM är ett tillämpbart verktyg att utgå ifrån för att upprätthålla snäva vevaxeltoleranser. Användning av virtuell analysering istället för fysiska tester skulle medföra tidsbesparing och ha positiv inverkan på miljön.  Programvaran Abaqus används för genomförande av deformationsanalyser vilka också utvärderas mot fysiska mätningar i en dragprovmaskin (Instron) för att därigenom säkerställa pålitligheten av använd FE modell.  Analyser genomförs huvudsakligen för deformationsuppkomst av vevaxeln i samband med uppspänning. Två olika typer av vevaxlar analyseras. Till respektive vevaxel skapas en FE modell med ansatta randvillkor och belastningsförhållanden utgående från en genomförd mekanisk analys av vevaxeln. Erhållna resultat visar att bricksidorna av vevaxeln deformeras med i storleksordningen <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?10%5E%7B-2%7D" /> mm då vevaxeln belastas i samband med uppspänning med en hoptryckning på 0,2 mm. Denna deformation anses medföra risk att ett bearbetningsfel kan förorsakas. Analyserna visar även vilka ytor som deformeras mest/minst. Utvärdering mot dragprovning indikerar att riktning på vevaxeldeformation stämmer överens med analyserna, men att avvikelser på deformationsstorleken förekommer. Skillnaden kan möjligen förklaras med att E-modulen varierar inom den testade vevaxeln medan den definierade E-modulen i Abaqus antar ett konstant värde. Dessutom kan eventuella felkällor från dragprovningen ha inverkan på resultatutfallet av de fysiska mätningarna.  Genomförda analyser tyder på att FEM är tillämpbar för analysering av vevaxeldeformation och rekommendationer om en lämplig FE modell tillhandahålls. En potentiell lösning till deformationsproblemet anses vara beräkning av optimal klämkraft vid uppspänning. / Crankshaft deformation is studied in connection with clamping conditions in a whirl milling machine before a cutting process. The purpose of the project is to increase knowledge about the deformation behaviour of the crankshaft and its important functional surfaces by performing analyses using the finite element method (FEM). Volvo Cars in Skövde, Sweden is currently managing unwanted crankshaft deformation occurrence by using time consuming physical testing methods. Therefore, the company wish to use virtual analyses instead of physical tests. This work also leads to a determination if FEM is an applicable tool in order to maintain narrow tolerances of the crankshaft. Using virtual analyses instead of physical tests would be time saving and would also have a positive impact on the environment. The computer software Abaqus is used to implement the deformation analyses that are also evaluated against physical measurements done with a tensile testing machine (Instron) and thereby be able to ensure the reliability of the used FE model. FE analyses are mainly performed to evaluate the deformation of the crankshaft associated with clamping. Two different crankshaft types are being analysed. A FE model is created for each crankshaft along with applied boundary and load conditions according to performed mechanical analysis of the crankshaft. Obtained results show that the thrust bearing sides of the crank pins on the crankshaft deform in the range of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?10%5E%7B-2%7D" /> mm when the crankshaft is compressed during clamping with 0.2 mm. This deformation is considered to entail a risk for a processing error to occur. At the same time the analyses show which surfaces are most/least deformed. Evaluation according to the tensile testing indicates that the direction of the crankshaft deformation corresponds to the analysis but slight deviation of the deformation magnitude is present. The deviations can be explained by variations of the E-module within the crankshaft while the defined E-module in Abaqus has a constant value. Furthermore, there is a possibility that sources of error from the tensile tests can have an influence on the obtained results from the physical measurements. Conducted analyses indicates that FEM is applicable for crankshaft deformation analyses and recommendations of a suitable FE model are provided. A potential solution of the deformation problem is considered to be the calculation of optimal clamping force.

La modélisation des efforts de coupe en usinage est nécessaire pour prédire certaines caractéristiques de la pièce usinée comme sa géométrie, son état de surface ou encore l'intégrité de la matière en sub-surface.Les nombreux modèles d'efforts de coupe déjà développés sont souvent appliqués dans le cas d'opérations d'usinage simples, ce qui limite leur diffusion vers le milieu industriel, alors qu'il existe un réel besoin de modélisation d'opérations d'usinage complexes et variées, et prenant en compte d'éventuels changements métallurgiques au niveau du matériau usiné.L'objectif de ces travaux est de proposer un modèle d'efforts de coupe appliqué à toute opération de tournage d'une part et considérant certaines propriétés mécaniques du matériau usiné d'autre part.Concernant l'aspect multi-opérations, un modèle géométrique utilisant des transformations homogènes a été développé et permet de décrire à la fois la trajectoire et la géométrie de l'outil. Les effets de paramètres originaux, tels que le diamètre de la pièce, l'angle de direction d'arête et le rayon de bec, sont étudiés, notamment à l'aide de nouvelles configurations de coupe élémentaires. La prise en compte de ces paramètres dans les relations de coupe locales permet finalement d'améliorer la simulation des efforts de coupe lors d'un contournage.L'approche utilisée pour l'aspect multi-matériaux consiste à modifier progressivement le matériau usiné. Ainsi, le matériau initial, le cuivre pur, a été étudié dans différents états métallurgiques, obtenus par des traitements thermo-mécaniques. En particulier, le procédé d'extrusion coudée à aires égales (ECAE) a été utilisé afin d'écrouir le matériau dans la masse. Ainsi, trois matériaux aux caractéristiques mécaniques différentes mais conservant plusieurs caractéristiques communes (thermiques notamment) ont pu être comparés en termes d'efforts de coupe. Les coefficients des relations de coupe sont finalement mis en regard des propriétés mécaniques obtenues par des essais de traction et de compression à grande vitesse. / The cutting forces have to be known as accurately as possible in order to predict the characteristics of the workpiece as the geometry, the roughness or the material integrity.Numerous models have been yet developed; however, the majority cannot be used for the various industrial cutting operations and remain confined for a single machined material.The objective of this study is to develop a cutting forces model applied to any turning operation and taking into account some mechanical characteristics of the machined material.First, a geometrical model based on homogeneous transformations is presented. Then, the effects of some parameters, like the workpiece diameter, the cutting edge angle and the nose radius, are studied by using new cutting configurations, in order to improve the cutting laws.The multi-material aspect is approached by modifying the metallurgical state with thermo-mechanical treatments, especially by using the equal channel angular extrusion process in order to harden the material in the mass. Finally, the coefficients of the local cutting relations are compared to mechanical characteristics obtained from tensile and high compression tests.

Cette étude porte sur l'usinage de l'alliage de titane Ti17 avec une assistance jet d'eau haute pression. Une attention particulière a été portée à l'analyse des mécanismes de dégradation et d'usure des outils lors de l'usinage avec et sans assistance. Le suivi de l'usure est réalisé par des observations régulières au microscope électronique à balayage (MEB) et par des analyses chimiques (technique EDS) afin de déterminer les zones de dépôt de matière sur l'outil. Toutes ces observations ont permis d'expliquer les mécanismes d'usure pour une opération d'ébauche et de finition. Il a été montré que les mécanismes d'usure sont différents entre l'usinage conventionnel et l'usinage assisté. En effet, lors de l'assistance jet d'eau haute pression, certains mécanismes ne sont plus activités mais d'autres mécanismes sont accélérés. Il existe donc une pression de jet d'eau optimale pour minimiser l'usure de l'outil.Afin de mettre en évidence l'effet du jet d'eau sur les phénomènes thermomécaniques dans les zones de formation du copeau, une modélisation par éléments finis est réalisée. Un couplage fluide / structure a dû être mis en place afin de prendre en compte les actions mécaniques et thermiques du jet d'eau sur la zone de coupe. Pour cela, la loi de comportement et le modèle d'endommagement de Johnson-Cook, ont été identifiés pour le Ti17 dans des conditions extrêmes sur une large gamme de températures et de vitesses de déformation. Cette modélisation a permis de mettre en évidence, pour l'usinage assisté haute pression, la diminution de la zone de contact outil/copeau, de retrouver la fragmentation du copeau et de quantifier le refroidissement des différentes zones de cisaillement.En revanche, cette modélisation ne permet pas de connaître l'effet de l'hétérogénéité microstructurale du matériau sur la zone de coupe. Ce constat est d'autant plus important que le matériau étudié présente une taille de grain importante (de l'ordre du millimètre). Pour cela, une nouvelle modélisation (multi-échelle) a été développée afin de prendre en compte la microstructure du matériau. Le matériau est donc modélisé comme un polycristal qui prend en compte des lois de la plasticité cristalline. Cette nouvelle approche permet alors de simuler la formation du copeau en prenant en compte les orientations cristallines des grains et les changements de phase qui apparaissent lors de l'usinage. / This study focuses on the machining of the Ti17 titanium alloy using high-pressure water jet assistance. Special emphasis is placed on the analysis of degradation mechanisms and tool wear during machining, with and without assistance. Wear monitoring was achieved by regular observations using both scanning electron microscope (SEM) and chemical analysis (EDS technique) to determine the areas of material deposition on the tool. These observations made it possible to explain the wear mechanisms for roughing and finishing conditions. Wear mechanisms for conventional machining and for assisted machining were found to be significantly different. Indeed, with high-pressure water jet assistance, some tool wear mechanisms are no longer activated, whereas others are accelerated. Hence, there exists an optimum water jet pressure which minimizes tool wear.To highlight the effect of water jet assistance on the thermomechanical phenomena in the chip formation zone, finite-element modeling has been performed. Fluid/structure coupling was developed to take into account the mechanical and thermal effects of the water jet. For this to be possible, the Johnson-Cook constitutive law and damage model have been identified for the Ti17 titanium alloy, under extreme conditions, over a wide range of temperatures and strain rates. This modeling has highlighted the fact that, for high-pressure assisted machining, the tool/chip contact zone is reduced. In addition, the simulation of chip fragmentation as well as the cooling effect on the tool and workpiece is possible.However, this model does not shed light on the effect of the microstructural heterogeneity of the material in the cutting zone. This is an important observation because the material studied has a very large grain size (of the order of a millimeter). For this reason, a new (multi-scale) modeling approach has been developed to take into consideration the microstructure of the material. The material is subsequently modeled as a polycrystal which obeys crystal plasticity constitutive laws. This new approach is then used to simulate chip formation, taking into account the grain orientations and phase changes that occur during the machining process.

Aujourd'hui, les méthodes de corrélation d'images sont largement utilisées pour la caractérisation et le suivi temporel des essais mécaniques. Cependant dans le domaine de l'usinage, ces méthodes sont très peu employées pour l'étude en pointe d'outil de la coupe par manque d'accessibilité, de la faible taille de la zone observée et des fortes déformations dans la zone de coupe. Dans cette thèse, nous mettons en application la technique de corrélation d'images pour l'étude et la caractérisation des champs cinématiques induits dans la matière usinée, durant des essais de coupe conduits avec des conditions opératoires représentatives des opérations industrielles. Ces conditions nous ont permis de développer, en premier lieu, des outils expérimentaux et numériques. Puis, les performances du dispositif expérimental ainsi que les incertitudes de corrélation ont été quantifiées. Différentes stratégies d'exploitation des images ainsi que des outils numériques pour la mesure des caractéristiques de la coupe sont proposés. Ensuite, nous avons développé un outil de corrélation d'images intégrée pour la mesure des efforts dynamiques grâce à un modèle analytique. Pour valider l'ensemble des méthodes, des essais de rabotage, d'abord dans un alliage d'aluminium, puis dans un acier 100~CrMo~7 traité thermiquement, ont été conduits. Ils ont permis de quantifier les champs cinématiques ainsi que les caractéristiques de la coupe. Enfin ces outils ont été appliqués pour la prédiction de l'intégrité de surface engendrée par une géométrie 3D d'outil de coupe dans le matériau dur. / Nowadays, digital image correlation (DIC) methods are widely employed to the mechanical testing characterization and their temporal monitoring. However in the machining field, to study the cutting process at the tool edge, these methods are not commonly applied due to the poor accessibility, the size of the observed area and the large strain occurring herein. In this study, the kinematic fields induced in the material by the cutting process are characterized and analyzed at industrial cutting conditions. In order to take and treat the pictures of the cut, experimental and numerical techniques have been first established. Then, the experimental setup performances and the uncertainties of the DIC were quantified. Different images selection strategies for the DIC and numerical post-processing algorithm for measuring the characteristics of the cut were proposed. Furthermore, a DIC integrated approach based on an analytical model was developed to record dynamics cutting forces. Trials in orthogonal configuration were performed and analyzed to validate the developed procedures first in an aluminium alloy, then in a 100~CrMo~7 hardened steel. The kinematics fields and the macroscopic data of the cut were successfully measured thanks to these tools. Finally, they were used for the prediction of the surface integrity induced by a 3D cutting edge in the hard material.

Ce travail de thèse se concentre sur l’étude du comportement dynamique des tubes minces durant leur usinage par tournage et notamment sur la survenue du broutement régénératif. L’étude de l’usinage de ce type de pièce est pertinente car ces pièces font l’objet d’une large diffusion dans divers domaines industriels tels que la construction aéronautique (notamment moteurs), la construction navale, la production de fusées. Ces pièces ayant une faible rigidité, il est fréquent que des vibrations indésirables se produisent en cours d’usinage. Il est donc intéressant d’être à même de les prédire pour les éviter.L’approche proposée vise à permettre un choix rapide et efficace des conditions de coupe, et notamment des profondeurs de passe, pour cette opération d’usinage. Pour cela nous proposons de mettre en place un modèle mécanique analytique du tube (modèle de coque mince utilisant un nombre réduit de degrés de liberté) de manière à réduire les coûts numériques et à faciliter l’analyse du phénomène. L’impact de la taille du modèle sur les résultats est étudié (nombre de formes propres) ainsi que de la prise en compte de l’enlèvement de matière (évolution du comportement dynamique) et du déplacement de l’outil. Afin de valider l’approche une expérience a été mise en place et est également présentée dans ce mémoire. / This work focuses on the study of the dynamic behavior of thin tubes during their machining by turning and gives particular emphasis on the occurrence of regenerative chatter. The study of machining of this type of workpiece is relevant because they are widely used in various industrial fields such as aircraft construction (including engines), shipbuilding, rocket production. As these parts have low rigidity, it is common that undesirable vibrations occur during machining. It is therefore of interest to be able to predict them in order to avoid them.The proposed approach is designed to enable a fast and efficient selection of cutting conditions, including cutting depths for this machining operation. We thus propose to elaborated an analytical model for the dynamics of the tube (thin shell based model using a reduced number of degrees of freedom) to reduce the numerical costs and to facilitate the analysis of the phenomenon. The impact of the size of the model on the results is studied (number of shape functions), as well as the impact of material removal (evolution of the dynamic behavior) and of the motion of the tool. An experiment, presented in this thesis, was also set up in order to validate the approach.

There is a strong industrial driving force to find alternative production technologies in order to make the production of aero engine components of superalloys even more efficient than it is today. Introducing new and nonconventional machining technologies allows taking a giant leap to increase the material removal rate and thereby drastically increase the productivity. However, the end result is to meet the requirements set for today's machined surfaces.The present work has been dedicated to improving the knowledge of how the non-conventional machining methods Abrasive Water Jet Machining, AWJM, Laser Beam Machining, LBM, and Electrical Discharge Machining, EDM, affect the surface integrity. The aim has been to understand how the surface integrity could be altered to an acceptable level. The results of this work have shown that both EDM and AWJM are two possible candidates but EDM is the better alternative; mainly due to the method's ability to machine complex geometries. It has further been shown that both methods require post processing in order to clean the surface and to improve the topography and for the case of EDM ageneration of compressive residual stresses are also needed.Three cold working post processes have been evaluated in order to attain this: shot peening, grit blasting and high pressure water jet cleaning, HPWJC. There sults showed that a combination of two post processes is required in order to reach the specified level of surface integrity in terms of cleaning and generating compressive residual stresses and low surface roughness. The method of high pressure water jet cleaning was the most effective method for removing the EDM wire residuals, and shot peening generated the highest compressive residual stresses as well as improved the surface topography.To summarise: the most promising production flow alternative using nonconventional machining would be EDM followed by post processing using HPWJC and shot peening.

Le perçage assisté par vibrations est un procédé assurant la maîtrise dimensionnelle des copeaux pour gagner en fiabilité sur les opérations de perçage. L’ajout d’une oscillation axiale pilotée en amplitude et en fréquence introduit deux nouveaux paramètres à déterminer en adéquation avec les paramètres conventionnels que sont l’avance et la vitesse de coupe. Le paramétrage d’une telle opération n’est donc pas trivial. Afin de fournir un outil d’optimisation du paramétrage du procédé, une nouvelle modélisation prenant en compte l’environnement « Pièce-Outil-Machine » est proposée. L’intégration de la géométrie de l’outil, des spécificités des interactions entre l’Outil et la Matière, et du comportement dynamique de la Machine permet s’adapter aux conditions de mise en oeuvre du procédé. Une méthode d’identification dissociée des éléments de l’environnement « Pièce-Outil-Machine » permet de caractériser les spécificités de chacun de ces éléments. Cette modélisation est validée par une campagne d’essai. La modèle développé dans ces travaux permet donc de prédire le comportement du procédé en vue d’une optimisation des paramètres opératoires. / Vibrations assisted drilling is a process which ensures chip shape control in order to increase reliability during drilling operations. The adding of axial oscillation, controlled with amplitude and frequency, introduce two new parameters which must determinate according to the conventional parameters (feed and speed rotation). The optimal setting of vibrations assisted drilling is not obvious. To provide an optimization-tool of the process, a new model which take into account the “Tool-Workpiece-Machine” environment, is proposed. Drill geometry, Tool-Workpiece interactions and dynamic behavior of the Machine are incorporated in the model. Tis specificity allows adjusting behavior of the process with the case of application. An identification methodology is presented to characterize the environment. Simulation’s results and experimental results are compared to validate the model. This model thus allows predicting process behavior in order to optimize the operational parameters.

With the emerging development of new technology and the constantly falling prices, more companies will find interest in industrial robots. Until today, the typical robot users have been large scale car manufacturers. But there exists a big potential market within the small to medium businesses that already uses of CNC machines. Attracting smaller businesses to start using industrial robots could open up the doors to new possibilities and increase their production. Unfortunately, most people still lack the knowledge of operating and programming industrial robots. But many companies have knowledge in G-code which is normally used in CNC machines. That is why this work is focussing on the development of a software that opens up the possibility to make use of G-code to program advanced robot paths with minimal user input. By striving for easier handling of robots, the vision about a more efficient and automated society will become one step closer. The introduction straightens out the different basic principles of CNC milling machines and robots. This will introduce the reader and highlight the different similarities and differences that exist between robots and CNC mills. The goal of this work has been to create an add-in application for ABB’s off-line programming software RobotStudio that was able to import at least one type of file format commonly used for CNC milling. The program should be able to handle some basic functionality, the focus has been on the standard iso6983 type of G-code. The project started with a literature study that gave the author a better insight in both the previous research within the area but also deeper knowledge of the systems CNC mills and robots. The work continued with the development of a software able to import the specified file format. The software has been built in C# and is built as an add-in software for ABB’s offline programming software RobotStudio. The result presents a software that is able to read different types of G-code and translate them into generated paths in RobotStudio. The software also has an inbuilt function in order to parameterize the G02 and G03 commands that represent curves in G-code into straight line segments of the type MoveL in RobotStudio.

This thesis presents cutter swept volume generation, in-process workpiece modeling and Cutter Workpiece Engagement (CWE) algorithms for finding the instantaneous intersections between cutter and workpiece in milling. One of the steps in simulating machining operations is the accurate extraction of the intersection geometry between cutter and workpiece. This geometry is a key input to force calculations and feed rate scheduling in milling. Given that industrial machined components can have highly complex geometries, extracting intersections accurately and efficiently is challenging. Three main steps are needed to obtain the intersection geometry between cutter and workpiece. These are the Swept volume generation, in-process workpiece modeling and CWE extraction respectively. In this thesis an analytical methodology for determining the shapes of the cutter swept envelopes is developed. In this methodology, cutter surfaces performing 5-axis tool motions are decomposed into a set of characteristic circles. For obtaining these circles a concept of two-parameter-family of spheres is introduced. Considering relationships among the circles the swept envelopes are defined analytically. The implementation of methodology is simple, especially when the cutter geometries are represented by pipe surfaces. During the machining simulation the workpiece update is required to keep track of the material removal process. Several choices for workpiece updates exist. These are the solid, facetted and vector model based methodologies. For updating the workpiece surfaces represented by the solid or faceted models third party software can be used. In this thesis multi-axis milling update methodologies are developed for workpieces defined by discrete vectors with different orientations. For simplifying the intersection calculations between discrete vectors and the tool envelope the properties of canal surfaces are utilized. A typical NC cutter has different surfaces with varying geometries and during the material removal process restricted regions of these surfaces are eligible to contact the in-process workpiece. In this thesis these regions are analyzed with respect to different tool motions. Later using the results from these analyses the solid, polyhedral and vector based CWE methodologies are developed for a range of different types of cutters and multi-axis tool motions. The workpiece surfaces cover a wide range of surface geometries including sculptured surfaces. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate